ANCELOT B
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is the latest release of
LANCELOT,
and is designed to solve
large-scale optimization problems involving the minimization of a
nonlinear objective, subject (perhaps) to linear or nonlinear equality
and box constraints. All functions involved are assumed to be
group partially separable, and the minimization is based on a
Sequential Augmented Lagrangian algorithm. The new release is coded in
Fortran 95, allows for a non-monotone descent strategy,
Moré and Toraldo-type projections, optional use of Lin
and Moré's
ICFS
preconditioner, structured trust regions, and more.
ANCELOT_SIMPLE
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is a simple-minded interface to LANCELOT for small, dense problems.
ILTRANE
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is a package for finding a feasible point for a set of
linear and/or nonlinear equations and inequalities using
a multi-dimensional filter trust-region approach. In the event
that the system is inconsistent, a local measure of infeasibility
is minimized. Core linear algebraic
requirements are handled by an adaptive preconditioned
CG/Lanczos iteration.
PB
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solves quadratic programs using a primal-dual interior-point
method globalized by means of a trust region. The method
works in two phases, the first finding a feasible point for
the set of constraints, while the second maintaining feasibility
while iterating towards optimality. Once again, core linear algebraic
requirements are handled by an adaptive preconditioned
CG/Lanczos iteration.
PA
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is an active-set quadratic programming solver which can also
treat l_1 quadratic programs. At each iteration, a step is
computed along a direction which solves an equality-constrained
quadratic program whose constraints are defined by a working
subset of the currently active constraints. Although, in general, QPB
is to be preferred, QPA is most useful when warm-starting a
perturbation of a previously-solved problem.
PC
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is a crossover quadratic programming solver which applies
successively QPB and QPA. The former is used to obtain a
good estimate of the solution at low cost, while the latter
refines the solution. Of particular note, the optimal active set
given by QPC is more reliable than that from QPB.
RESOLVE
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is a quadratic program preprocessor. It aims to
apply inexpensive transformations to a given quadratic
program, so as to simplify it before passing it to one of the
other GALAHAD solvers. Once the solver has completed its
task, a post-processing stage may be used to recover the
original problem and its solution.
SQP
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uses a primal-dual interior-point method to solve a linear or
separable convex quadratic program. Alternatively, it may
also be used to compute the analytic center of the feasible
set, if it exists.
CP
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uses a primal-dual interior-point method to find a well-centered
interior point for a region defined by a finite number of
linear equality and inequality constraints. If the region is
feasible but has no interior, inequality constraints which
must always be active are identified.
LTR
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solves the problem of minimizing a quadratic subject to an
ellipsoidal trust-region constraint, using a Krylov method.
The algorithm does not require
any factorization of the Hessian and may also be used to
minimize the quadratic over the boundary of the trust
region.
LRT
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solves the problem of minimizing a quadratic subject plus
a regularisation term penalising a weighted two-norm of the
variables, using a Krylov method. Again, the algorithm does not
require any factorization of the Hessian.
STR
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solves the problem of minimizing the two-norn of the
deviation Ax-b subject to an ellipsoidal trust-region
constraint, using a Krylov method.
The algorithm does not require any factorization of A.
SRT
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solves the problem of minimizing the square of the two-norn of the
deviation Ax-b plus a regularisation term penalising
the two-norm of the variables, using a Krylov method.
Again, the algorithm does not require any factorization of A.
2RT
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solves the problem of minimizing the two-norn of the
deviation Ax-b plus a regularisation term penalising
the two-norm of the variables, using a Krylov method.
Once again, the algorithm does not require any factorization of A.
QP
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solves quadratic programming problems for which all
the constraints are equations.
DC
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determines whether a system of linear equations is of full rank,
and identifies a maximal subset which may be removed without changing
the rank
BLS
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provides a variety of preconditioners which may be applied
when solving saddle point (alternatively augmented, KKT) systems
of linear equations.